Differential equations and linear algebra (Fourth edition)

Abstract

The evolution of the present text is based on experience teaching in ferential equations and linear algebra with an emphasis on conceptual ideas and troductory difthe use of applications and projects to involve students in active problem-solving experiences. Technical computing environments like Maple, Mathematica, MATLAB, and Python are widely available and are now used extensively by practicing engineers and scientists. This change in professional practice motivates a shift from the traditional concentration on manual symbolic methods to coverage also of qualitative and computer-based methods that employ numerical computation and graphical visualization to develop greater conceptual understanding. A bonus of this more comprehensive approach is accessibility to a wider range of more realistic applications of differential equations. Both the conceptual and the computational aspects of such a course depend heavily on the perspective and techniques of linear algebra. Consequently, the study of differential equations and linear algebra in tandem reinforces the learning of both subjects. In this book we therefore have combined core topics in elementary differential equations with those concepts and methods of elementary linear algebra that are needed for a contemporary introduction to differential equations